Gradient Index Optics

Gradient Index Optics deals with the application of gradients in optical systems of classical types: gradient index lenses. The emphasis is on the theory and practice related to gradient index lenses. Only isotropic media are considered since they are the ones for which the refractive index at each point is independent of direction.

Comprised of 12 chapters, this book begins with a historical background on the use of gradients in astronomy and developments in gradient index lenses, along with the underlying basic theory. The discussion then turns to spherical gradients, paying particular attention to rays, Maxwell's fisheye lens, the Luneburg lens, and astronomical refraction. Subsequent chapters focus on the ray trace in a spherical gradient; axial gradients and their use as an anti-reflection coating; radial gradients and ray tracing in a radial gradient; and fundamentals of aberration theory. The wood lens and ray trace in a general medium are also considered, together with methods for fabrication of gradient elements and measurement of index gradients using an approximate method and interferometric methods.

This monograph will be of interest to physicists.

Preface

Chapter 1 Historical Introduction

1.1 Gradients in Astronomy

1.2 Gradient Index Lenses

1.3 Recent Developments

1.4 Basic Theory

Chapter 2 Spherical Gradients

2.1 Introduction

2.2 Determining the Rays

2.3 Maxwell's Fisheye Lens

2.4 The Luneburg Lens

2.5 The Generalized Luneburg Lens

2.6 Astronomical Refraction

Chapter 3 Ray Trace in a Spherical Gradient

3.1 Basic Equations

3.2 Improving the Ray-Trace Formulas

3.3 Finding the Direction of the Ray

3.4 Technical Considerations

3.5 Summary

3.6 Numerical Example

3.7 Other Examples

Chapter 4 Axial Gradients

4.1 Introduction

4.2 Equations of the Rays

4.3 A Special Axial Gradient

4.4 Wave Optics Considerations

4.5 Axial Gradient as an Antireflection Coating

Chapter 5 Radial Gradients

5.1 Basic Equations

5.2 Practical Considerations

5.3 A Special Radial Gradient

5.4 The GRIN Rod Problem

Chapter 6 Ray Tracing in a Radial Gradient

6.1 Introduction

6.2 Paraxial Ray Trace

6.3 Special Trace for Meridional Rays

6.4 A Perturbation Tracing Method

6.5 Third-Order Trace

Chapter 7 Aberration Theory

7.1 Basic Concepts

7.2 Total Aberrations

7.3 Buchdahl Theory

Chapter 8 The Wood Lens

8.1 Introduction

8.2 The Photographic Wood Lens

8.3 The Thin Wood Lens

Chapter 9 More General Media

9.1 Rotation-Symmetric Gradient

9.2 A Practical Ray-Tracing Routine

9.3 Ray Trace in a General Medium

Chapter 10 Lens Design with Gradient

10.1 General Comments

10.2 A Simple Axial-Gradient Lens

10.3 Paraxial Rays in a Gradient Singlet

10.4 Designing Gradient Singlets

10.5 A Spherical-Gradient Singlet

10.6 Replacing Aspherics by Gradients

10.7 A Simple Image Inverter

Chapter 11 Fabrication of Gradient Elements

11.1 The Diffusion Method

11.2 Other Methods

Chapter 12 Measurement of Index Gradients

12.1 An Approximate Method

12.2 Interferometric Methods

Appendix A Derivation of Equations (1.8)

Appendix B Verification of Tracing Formulas for a Spherical Gradient

Appendix C Derivation of Third-Order Tracing Formulas for a Radial Gradient

Appendix D Derivation of Equations (10.10) to (10.16)

References

Index